As an image processing technique for random noise reduction in an image, a BM3D with shape-adaptive PCA (BM3D-SAPCA) method, for instance, has been proposed. In the BM3D-SAPCA method, a principal component analysis of a reference block being a set of local N pixels in an image and periphery blocks collected from around the reference block, which is similar to the reference block, is conducted, and d basis patterns of which eigenvalues are equal to or greater than a certain thresholds are selected from among obtained N basis patterns. The reference block and the periphery blocks are projected to a subspace defined by the selected d basis patterns, and with respect to d1 projection coefficients obtained for each block, one or more projection coefficients of which absolution values are smaller than a certain threshold t are replaced with zero. By having each block reconstructed by a linear sum of the d1 basis patterns using renewed projection coefficients, it is possible to reduce noise from the reference block and the periphery blocks.
As another image processing technique for random noise reduction in an image, a non-local PCA method has been proposed. In the non-local PCA method, a weighted principal component analysis in which a similarity between periphery blocks being similar to a reference block and the reference block is used as a weight is executed for the periphery blocks, and d2 basis patterns of which eigenvalues are equal to or greater than a certain threshold as are selected from among obtained N basis patterns. The reference block is projected to a subspace defined by the selected d2 basis patterns, and by having the reference block reconstructed by a linear sum of the d2 basis patterns using obtained d2 projection coefficients, noise in the reference block can be reduced.